Connectivity-Optimized Representation Learning via Persistent Homology

Roland Kwitt, Christoph Hofer, Marc Niethammer, Mandar Dixit

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragForschungBegutachtung

Abstract

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder’s latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.
OriginalspracheEnglisch
TitelProceedings of Machine Learning Research
UntertitelProceedings of the 36th International Conference on Machine Learning
Seiten2751-2760
Seitenumfang9
Band97
PublikationsstatusVeröffentlicht - 2019
VeranstaltungInternational Conference on Machine Learning - Long Beach Convention & Entertainment Center, Long Beach, California, USA/Vereinigte Staaten
Dauer: 10 Jun 201915 Jun 2019

Konferenz

KonferenzInternational Conference on Machine Learning
KurztitelICML
LandUSA/Vereinigte Staaten
OrtLong Beach, California
Zeitraum10/06/1915/06/19

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Kwitt, R., Hofer, C., Niethammer, M., & Dixit, M. (2019). Connectivity-Optimized Representation Learning via Persistent Homology. in Proceedings of Machine Learning Research: Proceedings of the 36th International Conference on Machine Learning (Band 97, S. 2751-2760)